Numerical Analysis of the Fractional-Order Belousov–Zhabotinsky System

Abstract

This paper presents a new approach for finding analytic solutions to the Belousov–Zhabotinsky system by combining the Adomian decomposition method (ADM) and the homotopy perturbation method (HPM) with the Elzaki transform. The ADM and HPM are both powerful techniques for solving nonlinear differential equations, and their combination allows for a more efficient and accurate solution. The Elzaki transform, on the other hand, is a mathematical tool that transforms the system into a simpler form, making it easier to solve. The proposed method is applied to the Belousov–Zhabotinsky system, which is a well-known model for studying nonlinear chemical reactions. The results show that the combined method is capable of providing accurate analytic solutions to the system. Furthermore, the method is also able to capture the complex behavior of the system, such as the formation of oscillatory patterns. Overall, the proposed method offers a promising approach for solving complex nonlinear differential equations, such as those encountered in the field of chemical kinetics. The combination of ADM, HPM, and the Elzaki transform allows for a more efficient and accurate solution, which can provide valuable insights into the behavior of nonlinear systems.